Vibration energy harvesting via piezoelectric bimorph plates: An analytical model

Vibration energy harvesting using piezoelectric cantilevers has been widely studied during the past decade. As an alternative to piezoelectric cantilevers, plate-like energy harvesters can be much more effective in marine, aerospace, and automotive applications. This work presents an exact two-dimensional model that can be used for analyzing thin, moderately thick, and thick piezoelectric bimorph plate vibration harvesters. The model allows to consider for the substrate layer both homogenous materials, and those with varying properties along the thickness direction. For the latter case, porous materials with various porosity distributions are herein considered, and the piezoelectric layers are assumed to be wired in both parallel and series configurations. Rayleigh damping assumptions are also used to model the structural damping of the harvesting system. Using Hamilton's principle and Gauss's law, the energy harvesting model is established based on the first-order and the third-order shear deformation theories. Applying an analytical procedure to the electromechanical governing equations, closed-form steady-state response expressions, which relate the voltage output and the vibration response of the harvester to harmonic input force, are derived. Finally, the proposed model is validated, and the power generation performance of the plate harvester is discussed through conducting extensive parametric studies, covering the effect of design parameters, such as the applied electric load, porosity characteristics, electrical configuration, and geometrical parameters.